When two bodies of equal masses collide elastically then

Options

A. Linear momenta are exchanged
B. Velocities are exchanged
C. Speeds are exchanged
D. Slower body speeds up for and faster body slows down .

Explanation

To solve the problem of what happens when two bodies of equal masses collide elastically, we can break it down step by step.

### Step-by-Step Solution:

1. **Understanding Elastic Collision**:
- In an elastic collision, both momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy before the collision will be equal to the total momentum and total kinetic energy after the collision.

2. **Define the Masses and Initial Velocities**:
- Let the mass of each body be \( m \).
- Let the initial velocities of the two bodies be \( u_1 \) and \( u_2 \), where \( u_1 \) is the velocity of the first body and \( u_2 \) is the velocity of the second body.

3. **Collision Scenario**:
- Assume the first body is moving towards the second body. After the collision, the velocities of the two bodies will change.

4. **Final Velocities After Collision**:
- For two bodies of equal mass colliding elastically, the final velocities are exchanged. This means:
- The first body will have a final velocity of \( u_2 \).
- The second body will have a final velocity of \( u_1 \).

5. **Analysis of the Outcomes**:
- **Direction and Magnitude**: The direction of the velocities remains the same, but the magnitudes are exchanged.
- **Speeds Interchanged**: The speeds of the two bodies are interchanged after the collision.
- **Linear Momentum Exchange**: The linear momentum of the bodies before and after the collision is also exchanged. Initially, the momentum of the first body is \( m \cdot u_1 \) and for the second body is \( m \cdot u_2 \). After the collision, the first body has momentum \( m \cdot u_2 \) and the second body has momentum \( m \cdot u_1 \).
- **Speed Changes**: The slower body speeds up while the faster body slows down. For example, if one body was moving at 4 m/s and the other at 3 m/s, after the collision, the body that was moving at 3 m/s will now move at 4 m/s and vice versa.

### Conclusion:
All the statements regarding the outcomes of the elastic collision between two bodies of equal mass are correct:
- The direction and magnitude of velocities are maintained.
- Speeds are interchanged.
- Linear momenta are exchanged.
- The slower body speeds up and the faster body slows down.